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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function [dist, pos] = distancePointEdge(point, edge)
%DISTANCEPOINTEDGE Minimum distance between a point and an edge.
%
% DIST = distancePointEdge(POINT, EDGE);
% Return the euclidean distance between edge EDGE and point POINT.
% EDGE has the form: [x1 y1 x2 y2], and POINT is [x y].
%
% If EDGE is N-by-4 array, result is 1-by-4 array computed for each edge.
% If POINT is a N-by-2 array, the result is a N-by-1 array.
% If both POINT and EDGE are array, the result is computed for each
% point-edge couple, and stored into a NP-by-NE array.
%
% [DIST POS] = distancePointEdge(POINT, EDGE);
% Also returns the position of closest point on the edge. POS is
% comprised between 0 (first point) and 1 (last point).
%
% Eaxmple
% % Distance between a point and an edge
% distancePointEdge([3 4], [0 0 10 0])
% ans =
% 4
%
% % Distance between several points and one edge
% points = [10 15; 15 10; 30 10];
% edge = [10 10 20 10];
% distancePointEdge(points, edge)
% ans =
% 5
% 0
% 10
%
% % Distance between a point a several edges
% point = [14 33];
% edges = [10 30 20 30; 20 30 20 40;20 40 10 40;10 40 10 30];
% distancePointEdge(point, edges)
% ans =
% 3 6 7 4
%
%
% See also
% edges2d, points2d, distancePoints, distancePointLine
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2004-04-07
% Copyright 2004-2023 INRA - BIA-BIBS
% direction vector of each edge (row vectors)
vx = (edge(:, 3) - edge(:,1))';
vy = (edge(:, 4) - edge(:,2))';
% squared length of edges, with a check of validity
delta = vx .* vx + vy .* vy;
invalidEdges = delta < eps;
delta(invalidEdges) = 1;
% difference of coordinates between point and edge first vertex
% (NP-by-NE arrays)
dx = bsxfun(@minus, point(:, 1), edge(:, 1)');
dy = bsxfun(@minus, point(:, 2), edge(:, 2)');
% compute position of points projected on the supporting line, by using
% normalised dot product (NP-by-NE array)
pos = bsxfun(@rdivide, bsxfun(@times, dx, vx) + bsxfun(@times, dy, vy), delta);
% ensure degenerated edges are correclty processed (consider the first
% vertex is the closest)
pos(:, invalidEdges) = 0;
% change position to ensure projected point is located on the edge
pos(pos < 0) = 0;
pos(pos > 1) = 1;
% compute distance between point and its projection on the edge
dist = hypot(bsxfun(@times, pos, vx) - dx, bsxfun(@times, pos, vy) - dy);
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